Exponential Data

A(n) _________________ function will MULTIPLY the same number each time.

• Linear

• Quadratic

• Exponential

• All of the above

Which equation best fits the data in the table?

• y = 15940x - 2423.6

• y = 267.71x² -3494.46 + 16500

• y = 16500(0.80)^x

What function best fits the data in the table?

• linear

• exponential

• quadratic

Monica did an experiment to compare two method of warming an object. The results are shown in the table above. Which statement best describes her results?

• The temperature using both methods changed at a constant rate.

• The temperature using both methods changed at an exponential rate.

• The temperature using Method 2 changed at a constant rate.

• The temperature using Method 2 changed at an exponential rate.

Which statement is true based on the data in the table?

• f(x) is an exponential function

• g(x) is a linear function

• The y-intercept of g(x) is 10

• The slope of f(x) is 3

• A

• B

• C

• D

An investment of $1,200 is compounded continuously at an annual interest rate of 6%. Which function represents the amount, $ A $, after $ t $ years using the natural base $ e $?

• A(t) = 1200 \times (1.06)^t

• A(t) = 1200 \times e^{0.06t}

• A(t) = 1200 \times e^{6t}

• A(t) = 1200 + 0.06t

Answer explanation

The formula for continuous compounding is A(t) = Pe^{rt}, where P is the principal, r is the rate, and t is time. Here, P = 1200 and r = 0.06, leading to A(t) = 1200 × e^{0.06t}, which is the correct choice.

The population of a town grows according to the function $ P(t) = 3000 \times 1.04^t $, where $ t $ is in years. What is the annual growth rate in percentage?

• 1%

• 4%

• 40%

• 0.4%

Answer explanation

The population function is given by P(t) = 3000 × 1.04^t. The base of the exponent, 1.04, indicates an annual growth rate of 4%. Thus, the correct answer is 4%.

Given two points $(1, 150)$ and $(4, 1200)$ on an exponential function $ f(x) = ab^x $, find the value of $ b $.

• 2

• 2^{1/3}

• 3

• \sqrt{2}

Answer explanation

To find $ b $, use the points in the equation $ f(x) = ab^x $. From $ f(1) = 150 $ and $ f(4) = 1200 $, we get two equations: $ ab = 150 $ and $ ab^4 = 1200 $. Dividing gives $ b^3 = 8 $, so $ b = 2 $.

A function $ f(x) = 250 \times e^{0.04x} $ represents continuous growth. What is the growth rate expressed as a percentage?

• 0.04%

• 4%

• 40%

• 400%

Answer explanation

The function f(x) = 250 × e^(0.04x) indicates continuous growth with a growth rate of 0.04. To express this as a percentage, multiply by 100, resulting in 4%. Thus, the correct answer is 4%.